What did you do to celebrate Pi Day?

March 14th honored the number pi or “π” (3.1415926535…), the ratio of a circle's circumference to its diameter and one of the most intriguing concepts in mathematics. The intrigue is in the fact that it cannot be written as a fraction of two whole numbers and does not have a terminating or repeating set of decimals ... it goes on forever without repeating a pattern of the same numbers! A mysterious computer genius who goes by the name of "houkouonchi" owns the record for computing π to the most digits (13.3 trillion!). Maybe even more impressive is Akira Haraguchi, who holds the unofficial world record for memorizing the most digits (100,000!) in one sitting of 16 hours! Haraguchi views the memorization of π as a spiritual exercise, stating "To me, reciting pi’s digits has the same meaning as chanting the Buddhist mantra and meditating.”

In the world of mathematics, π is known as an "irrational" number given its bizarre attributes mentioned above. Similarly in the world of investing, investors sometimes are irrational when they do bizarre things that affect their investment pie.

We differentiate between two types of risks

(1) The real risk is a permanent loss of capital, resulting in a smaller investment pie and not meeting wealth planning goals.

(2) The fake risk relates to volatility, or how much the value of an investment moves up or down over a certain time period.

The first risk can be debilitating yet is something you can control, while the second variety is a permanent feature of the investment experience that is unavoidable.

We work hard to combat the true risk when investors get sucked into the fake risk.

This year is a great example of the harm in allowing fake risk to get in the way of true risk. In the chart [SS1] below, the gray bars represent the value of a portfolio (investment pie) that started with $1 million invested in the S&P 500 Index on December 31, 2015 (right axis). The green line represents the cumulative change in the portfolio value on each day based on the returns of the S&P 500 (left axis).

[SS1]Source chart

February 11th was the low of the year (so far), and the portfolio value was down to $894,879 or -10.5% from the original $1 million value. The S&P 500 Index has since recovered and was only down about 1% through March 11th.

If an investor were to sell on February 11th at the low point of the year and realize a permanent loss of capital that amounts to $105,121, the long-term effect on one's portfolio could be substantial. The difference between starting with $1 million versus $894,879 over 10- and 20-year periods assuming a 7.5% annual rate of return is shown below:

In Year 20, the damage to the pie turns out to be almost 50% of the original $1 million investment and a more than 10% hit to the final portfolio value of $4,247,851 … pretty much a whole slice!

Next time you find yourself contemplating doing something irrational in the midst of a market sell-off, our suggestion is to get your mind off the market, channel your inner-Haraguchi, and work on memorizing π ... or at least the first 50 digits!

*This material is for informational purposes only and is not intended to serve as a substitute for personalized investment advice or as a recommendation or solicitation of any particular security, strategy or investment product. The opinions expressed do not necessarily reflect those of author and are subject to change without notice. Past performance is not indicative of future results. Diversification cannot assure profit or guarantee against loss. There is no guarantee that any investment will achieve its objectives, generate positive returns, or avoid losses. Reference to an index does not imply that a portfolio will achieve return, volatility, or other results similar to an index. Performance of an index is not illustrative of any account, portfolio or strategy managed by Sequoia Financial Group. It is not possible to invest directly in an index.*